Hedging of options for jump-diffusion stochastic volatility models by Malliavin calculus

We study the locally risk minimizing approach in a market driven by jump-diffusion stochastic volatility models. We show that the Malliavin calculus, especially a jump-diffusion version of the Clark-Ocone formula, can generate the locally risk minimizing portfolio under weaker restrictions. This means thereafter we do not have to verify the strong condition V(t, s, y) is an element of C-1,C-2,C-2 and the differentiability condition V in s and y with bounded derivatives is sufficient. Also, this tool shortens calculations of the hedge.